ABOARD A U.S. GOVERNMENT AIRCRAFT (Reuters) -- U.S. Defense Secretary Robert Gates has said he would reassure Saudi Arabia this week that the kingdom would not suffer from Washington's efforts to improve its relations with Iran.

President Barack Obama's administration wants to engage diplomatically with Tehran, despite disagreements on a wide range of issues, most notably Iran's nuclear program.

The policy, a shift from the stance of George W. Bush's administration, has stirred unease among Gulf allies of the United States, who fear they could lose out if Washington builds a better relationship with Tehran.

But Gates, who visits Egypt and Saudi Arabia this week, said U.S. allies had no cause for concern and promised Washington would be "tough-minded" with Tehran if its overtures were rebuffed.

"One important message will be, particularly for the Saudis, that any kind of outreach to Iran will not be at the expense of our long-term relationships with Saudi Arabia and the other Gulf states that have been our partners and friends for decades," he said.

"We will deal with this in a sensible way and in a way that hopefully increases the security of everybody in the region, not just us," Gates told reporters aboard his plane as he flew from Washington to Cairo.

He said some fears among Gulf states may be based on "an exaggerated sense of what's possible" in relations between Washington and Tehran.

Gates, a former CIA director who served as Pentagon chief in the final years of the previous administration and was retained by Obama, has voiced skepticism about Iran's willingness to build better ties with the United States.

"While we're willing to reach out to the Iranians, as the president said, with an open hand, I think everybody in the administration from the president on down is pretty realistic and will be pretty tough-minded if we still encounter a closed fist," he said.

Gates said his two-day visit to Egypt, which includes a meeting with President Hosni Mubarak, was likely to touch upon the Israeli-Palestinian peace process and efforts by Egypt, with U.S. assistance, to curb smuggling into the Gaza strip.

"The Egyptians have played a huge role in terms of the Israeli-Palestinian problem, in trying to be a go-between and [to] try and help move that process forward," he said.